Gratuitous Rap

Basically, things like characters performing brief rap numbers in stories where it isn't the primary subject. Compare Piss-Take Rap and A Wild Rapper Appears.

Examples of Gratuitous Rap include:

Anime and Manga

Gintama: Katsura and his "Katsurap."
- Even more gratuitous are the recaps for the Thorny Boys arc.

Film

The masked slasher in Scary Movie dances around the room and dispenses some rapid-fire rap lyrics after the other characters invite him to smoke some marijuana. He even uses his knife to make "cool" rap gestures - but apparently gets a little too into it, because he ends up slashing everyone in the room to death.
Epic Movie contains several scenes.
Bulworth. A jaded politician decides to tell the truth, the whole truth and nothing but the truth to the American public... in rap...
- Significantly better than it sounds.
Titanic: The Legend Goes On. With the rapping dog.
Die, motherfucker, die, motherfucker, die!
- It works a little better here because the entire movie is set to hip-hop. Which is hiliarious because it's about weedy white (and one Indian) office workers.
The Hard Knock Life scene from the 3rd Austin Powers movie. Which also happened to be a parody of a rap by Jay-Z that sampled the soundtrack from Annie.
The infamous "Ninja Rap" sequence in Teenage Mutant Ninja Turtles II: The Secret of Ooze. Perpetrated by one and only Vanilla Ice.
Rapping shark in In Search Of The Titanic, making it two full length animated movies about Titanic disaster featuring rapping animals.
Yo, the name is Batty! The logic is erratic! Potato in a jacket! Toys in the attic! I rock and I ramble! My brain is SCRAMBLED! Rap like an animal, but I'm a mammal!
Care Bears in Wonderland. The rapping cat.
PIG POWER IN THE HOUSE!!!!
The Villain Song in The Muppets is a deliberately over-the-top example.

Live-Action TV

The Ringmaster in the Doctor Who serial "The Greatest Show in the Galaxy".
Degrassi Junior High constantly. The worst was Rick's environmental rap.

Web Comics

Minion Comics features a Teddy Ruxpin-esque stuffed turtle singing a rap song entitled "Punch Your Bitch In The Mouth" advising schoolchildren about how to treat their girlfriends.

Web Original

Commentary! The Musical, "Neil's Turn": in the middle of a song he suddenly starts rapping.

I'll charm the chicks (Are those real? Ha!)
Do magic tricks (Was it the three of spades? Ho!)
Lay down some tap
And I can rap
My name is Neil and I'm here to say, *random rapping noises*
No I can't rap
That was painful...

Homestuck, with GameBro, which doesn't seem to have any specific character performing it, but is a rap about an obscure plot element that resurfaces a negligible amount of times in the massive comic.

Western Animation

South Park gives us this little gem.

Cartman: Well I'm a Badass cowboy living in the cowboy days. A wiki wiki scratch yo yo jiggy jiggy. Me and Artemis Clyde frog from the big metal spider. A wiki wiki what.

Everybody's feelin' fine, 'cause it's party time!
"It's Spring Training, Charlie Brown" features one. Yes, a rap in a Peanuts special.
An episode of The Simpsons had Homer and Marge rap discipline to Bart. Maggie played beatbox. It was truly frightening.
- Homer also proposed a rap to advertise his Mr. Plow business.
The conclusion of an episode of Foster's saw Harriman make a rap video to promote the house on its "spider-web".
Dexter's Laboratory features an episode where Dexter raps about the "reality" behind Santa Claus.
We're the Mario Brothers, and plumbin's our game! We're not like the others who get all the fame!

Video Games